Efficient Array Pattern Synthesis via Polynomial Expansion With Determined Truncation Order

An efficient method based on dimensionality reduction is presented for array pattern synthesis. It describes array excitation distribution by utilizing a truncated Chebyshev polynomial expansion, then the dimension of the synthesis problem is significantly reduced from element number to the polynomial truncation order. Importantly, for an arbitrary planar array with specific shaping requirements, we propose a novel pattern-space projection method to accurately determine the truncation order, thus eliminating the need for inefficient and repeated synthesis attempts as before. Due to the precise and effective dimensionality reduction, pattern synthesis problem is greatly simplified. Then, alternating projection algorithm is applied to efficiently synthesize the polynomial coefficients whose dimension is much less than the array elements. Two examples of synthesizing different shaped patterns for planar arrays are conducted to validate the effectiveness and robustness.